... production¹

To appear in the Proceedings of the 6th International Symposium on Frontiers in Fundamental and Computational Physics (FFP6), September 26-29, Udine, ITALY

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... Sindoni²

potenzo17@yahoo.it

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... Ansoldi³

Email: ansoldi@trieste.infn.it

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... S. Ansoldi^3 4

Webpage: http://www-dft.ts.infn.it/$\sim$ansoldi

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... brane⁵

In the mathematical treatment of the classical situation the brane has, in fact, zero radius; from the physical point of view, with quantum gravity in mind, we can imagine this brane as a result of zero point quantum fluctuations.

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... brane⁶

We are going to consider $R$ as a function $R (\tau)$ of the proper time $\tau$ of an observer sitting on the brane and denote by an overdot the derivative with respect to $\tau$.

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... spacetime⁷

Since the compact notation could be misleading, we remember that we have two spacetimes with different cosmological constants $\Lambda _{\pm}$ and, thus, two metric functions $f _{\pm} (R)$; please, also remember the meaning of the square brackets defined above.

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